Espaces de Berkovich sur Z : étude locale

Details Espaces de Berkovich sur Z : étude locale Espaces de Berkovich sur Z : étude locale

2012-02-03

arxiv.org/abs/1202.0799v2

Mathematics

Algebraic Geometry

v2: Paper slightly reorganized. Added the proof that local rings are excellent for Berkovich spaces over Z

Scientific paper

We investigate the local properties of Berkovich spaces over Z. Using Weierstrass theorems, we prove that the local rings of those spaces are noetherian, regular in the case of affine spaces and excellent. We also show that the structure sheaf is coherent. Our methods work over other base rings (valued fields, discrete valuation rings, rings of integers of number fields, etc.) and provide a unified treatment of complex and p-adic spaces.

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